Recent advancements in technology have led to a deluge of big data streams that require real-time analysis with strict latency constraints. A major challenge, however, is determining the amount of resources required by applications processing these streams given their high volume, velocity and variety. The majority of research efforts on resource scaling in the cloud are investigated from the cloud provider's perspective with little consideration for multiple resource bottlenecks. We aim at analyzing the resource scaling problem from an application provider's point of view such that efficient scaling decisions can be made. This paper provides two contributions to the study of resource scaling for big data streaming applications in the cloud. First, we present a Layered Multi-dimensional Hidden Markov Model (LMD-HMM) for managing time-bounded streaming applications. Second, to cater to unbounded streaming applications, we propose a framework based on a Layered Multi-dimensional Hidden Semi-Markov Model (LMD-HSMM). The parameters in our models are evaluated using modified Forward and Backward algorithms. Our detailed experimental evaluation results show that LMD-HMM is very effective with respect to cloud resource prediction for bounded streaming applications running for shorter periods while the LMD-HSMM accurately predicts the resource usage for streaming applications running for longer periods.